For each contact there is a personal address field which can be filled with informations like street name, city, country, and so on. The problem is that in order to display these informations on a map, Google maps have to do an online search to get the coordinates. How can I use this feature offline ?
Short answer is: you can't.
The feature relies on a service called geocoding, which is done on Google's servers. The only possibility for this to be done locally would be to download the entire map data to the device and use that data to calculate the coordinates from an address. This is a resource and space consuming task (for example, OpenStreetMap has a dataset of 370GB), and not suitable for mobiles.
A workaround would be to save the coordinates themselves as a street address in the form
62.244858,25.758712 in addition to the regular address and use this "address" to show the map. The catch is, you'd still have to use a geocoder to resolve the address to coordinates.
All address fields are sent to Google to be resolved, that's why the workaround I suggested is invalid.